class_docstr: Binary Gaussian process classification based on Laplace approximation.
  
  The implementation is based on Algorithm 3.1, 3.2, and 5.1 of
  ``Gaussian Processes for Machine Learning'' (GPML) by Rasmussen and
  Williams.
  
  Internally, the Laplace approximation is used for approximating the
  non-Gaussian posterior by a Gaussian.
  
  Currently, the implementation is restricted to using the logistic link
  function.
  
  .. versionadded:: 0.18
  
  Parameters
  ----------
  kernel : kernel object
      The kernel specifying the covariance function of the GP. If None is
      passed, the kernel "1.0 * RBF(1.0)" is used as default. Note that
      the kernel's hyperparameters are optimized during fitting.
  
  optimizer : string or callable, optional (default: "fmin_l_bfgs_b")
      Can either be one of the internally supported optimizers for optimizing
      the kernel's parameters, specified by a string, or an externally
      defined optimizer passed as a callable. If a callable is passed, it
      must have the  signature::
  
          def optimizer(obj_func, initial_theta, bounds):
              # * 'obj_func' is the objective function to be maximized, which
              #   takes the hyperparameters theta as parameter and an
              #   optional flag eval_gradient, which determines if the
              #   gradient is returned additionally to the function value
              # * 'initial_theta': the initial value for theta, which can be
              #   used by local optimizers
              # * 'bounds': the bounds on the values of theta
              ....
              # Returned are the best found hyperparameters theta and
              # the corresponding value of the target function.
              return theta_opt, func_min
  
      Per default, the 'fmin_l_bfgs_b' algorithm from scipy.optimize
      is used. If None is passed, the kernel's parameters are kept fixed.
      Available internal optimizers are::
  
          'fmin_l_bfgs_b'
  
  n_restarts_optimizer: int, optional (default: 0)
      The number of restarts of the optimizer for finding the kernel's
      parameters which maximize the log-marginal likelihood. The first run
      of the optimizer is performed from the kernel's initial parameters,
      the remaining ones (if any) from thetas sampled log-uniform randomly
      from the space of allowed theta-values. If greater than 0, all bounds
      must be finite. Note that n_restarts_optimizer=0 implies that one
      run is performed.
  
  max_iter_predict: int, optional (default: 100)
      The maximum number of iterations in Newton's method for approximating
      the posterior during predict. Smaller values will reduce computation
      time at the cost of worse results.
  
  warm_start : bool, optional (default: False)
      If warm-starts are enabled, the solution of the last Newton iteration
      on the Laplace approximation of the posterior mode is used as
      initialization for the next call of _posterior_mode(). This can speed
      up convergence when _posterior_mode is called several times on similar
      problems as in hyperparameter optimization.
  
  copy_X_train : bool, optional (default: True)
      If True, a persistent copy of the training data is stored in the
      object. Otherwise, just a reference to the training data is stored,
      which might cause predictions to change if the data is modified
      externally.
  
  random_state : integer or numpy.RandomState, optional
      The generator used to initialize the centers. If an integer is
      given, it fixes the seed. Defaults to the global numpy random
      number generator.
  
  Attributes
  ----------
  X_train_ : array-like, shape = (n_samples, n_features)
      Feature values in training data (also required for prediction)
  
  y_train_: array-like, shape = (n_samples,)
      Target values in training data (also required for prediction)
  
  classes_ : array-like, shape = (n_classes,)
      Unique class labels.
  
  kernel_: kernel object
      The kernel used for prediction. The structure of the kernel is the
      same as the one passed as parameter but with optimized hyperparameters
  
  L_: array-like, shape = (n_samples, n_samples)
      Lower-triangular Cholesky decomposition of the kernel in X_train_
  
  pi_: array-like, shape = (n_samples,)
      The probabilities of the positive class for the training points
      X_train_
  
  W_sr_: array-like, shape = (n_samples,)
      Square root of W, the Hessian of log-likelihood of the latent function
      values for the observed labels. Since W is diagonal, only the diagonal
      of sqrt(W) is stored.
  
  log_marginal_likelihood_value_: float
      The log-marginal-likelihood of ``self.kernel_.theta``
docstr: Perform classification on an array of test vectors X.
  
  Parameters
  ----------
  X : array-like, shape = (n_samples, n_features)
  
  Returns
  -------
  C : array, shape = (n_samples,)
      Predicted target values for X, values are from ``classes_``
docstr_tok: ["Perform","classification","on","an","array","of","test","vectors","X.","Parameters","--","--","--","--","--","X",":","array-like",",","shape","=","(","n_samples",",","n_features",")","Returns","--","--","--","-","C",":","array",",","shape","=","(","n_samples",",",")","Predicted","target","values","for","X",",","values","are","from","``","classes_","``"]
code: def predict(self, X):
      """Perform classification on an array of test vectors X.
  
      Parameters
      ----------
      X : array-like, shape = (n_samples, n_features)
  
      Returns
      -------
      C : array, shape = (n_samples,)
          Predicted target values for X, values are from ``classes_``
      """
      check_is_fitted(
          self, ["X_train_", "y_train_", "pi_", "W_sr_", "L_"]
      )
  
      # As discussed on Section 3.4.2 of GPML, for making hard binary
      # decisions, it is enough to compute the MAP of the posterior and
      # pass it through the link function
      K_star = self.kernel_(self.X_train_, X)  # K_star =k(x_star)
      f_star = K_star.T.dot(
          self.y_train_ - self.pi_
      )  # Algorithm 3.2,Line 4
  
      return np.where(f_star > 0, self.classes_[1], self.classes_[0])
  
imports: import warnings
  from operator import itemgetter
  import numpy
  from scipy.linalg import cholesky, cho_solve, solve
  from scipy.optimize import fmin_l_bfgs_b
  from scipy.special import erf
  from sklearn.base import BaseEstimator, ClassifierMixin, clone
  from sklearn.gaussian_process.kernels import RBF, CompoundKernel, ConstantKernel
  from sklearn.utils.validation import check_X_y, check_is_fitted, check_array
  from sklearn.utils import check_random_state
  from sklearn.preprocessing import LabelEncoder
  from sklearn.multiclass import OneVsRestClassifier, OneVsOneClassifier
label_desc: Use image node_id 3 for calling the _BinaryGaussianProcessClassifierLaplace obj's underlying member method code with example usage: obj.predict(X) and returns: np